very do-able, we drove from Vegas to Zion to Bryce and then down to Page in one day. Your trip sounds much better!

We did this trip in reverse. We flew to Phoenix then travelled to Sedona, had 1 night but still managed to go on a trip of the area. Then went on to Kingman, Hoover Dam then on to Vegas. After couple nights in Vegas went on a 4 day bus tour. 1 night stay on Canyon rim 1 night Page overlooking Lake Mead and 1 night Bryce canyon. There were also trips to Monument Valley and Zion National park. The tour made sure you seen all places of interest. It was fantastic. We had plenty of free time to look around. We then returned and had another 2 nights in Vegas before flying home. This was all done in 11 days.We went in September and it was quite cold in Bryce and Zion due to it's elevation. Vegas was in mid 80's. So take jackets with you.
Whatever way you do this trip you will have a great time. We booked the 4 day trip through Travelscope.

@jvb1982: I agree with spirobulldog that 1 night tends to be enough for Monument Valley. Be sure to do a backcountry tour of some kind with a Navajo guide, either by horseback or 4x4. If you do take us up on the suggestion to lop 1 night off your Monument Valley leg, perhaps give Moab a 3rd night, or maybe head back to Flagstaff via Canyon de Chelly with an overnight there. Map ->: http://g.co/maps/99fyg Probably too late to get lodging in the park, but you might be able to find something in Chinle AZ http://bit.ly/IBTJBS Nothing luxurious, mind you, it is a reservation town after all, but the scenery at the canyon itself is beautiful.

No matter what you decide be sure to pick up an America the Beautiful Federal Lands Access Pass. For $80 this card gets you into all the National Parks and Monuments in the US for 1 year. Won't work at Monument Valley since it's a Navajo Tribal Park, but it will pay for itself on the trip you're proposing to take. Since you're coming from overseas, save the postage and pick it up at the first National Park Entrance Station you come to.